Q:
My question is what happens when two black holes with the
same mass, size and everything encounter each other? Question
two, what is a quasar?

A:
When two black holes encounter each other, they could form
another even more massive black hole. Multiple black holes
merging together is one idea scientists have proposed to
explain how mid-mass and supermassive black holes might be
created. That is, one way really massive black holes might be
formed is by two or more stellar black holes encountering
each other.

Quasars are galaxies with supermassive black holes at their
centers. Large amounts of material are falling onto a
quasar's supermassive black hole, which generates lots of
energy (light) that telescopes like Chandra can then observe.
Many galaxies are thought to contain supermassive black holes
at their centers (including our own galaxy, the Milky Way).
But in quasar galaxies, in addition to the supermassive black
hole, there is also a lot of material available for the black
hole to consume -- and so there's more energy produced.

Matter is consumed by a black hole when the gravitational
force of the black hole pulls it beyond the event horizon,
from which the matter cannot escape because the gravity is
too strong. The ultimate fate of the matter is unknown since
nothing, not even light, can escape from inside the event
horizon and give us information about what happened to the
material. The theory indicates that it must be crushed to an
extremely high density -- to a point at which the theory no
longer applies! However, since nothing can escape from a
black hole, all energy and mass of the matter is captured
inside of the black hole. According to the theory, this
energy and mass is not destroyed, though it may change forms.